Defining the Pose of any 3D Rigid Object and an Associated Distance

Romain Brégier (1, 2) , Frédéric Devernay (1) , Laetitia Leyrit (2) , James L. Crowley (3)

1 IMAGINE - Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments
2 Siléane [Saint-Etienne]
3 PERVASIVE - Interaction située avec les objets et environnements intelligents

The pose of a rigid object is usually regarded as a rigid transformation, described by a translation and a rotation. However, equating the pose space with the space of rigid transformations is in general abusive, as it does not account for objects with proper symmetries -- which are common among man-made objects. In this article, we define pose as a distinguishable static state of an object, and equate a pose with a set of rigid transformations. Based solely on geometric considerations, we propose a frame-invariant metric on the space of possible poses, valid for any physical rigid object, and requiring no arbitrary tuning. This distance can be evaluated efficiently using a representation of poses within an Euclidean space of at most 12 dimensions depending on the object's symmetries. This makes it possible to efficiently perform neighborhood queries such as radius searches or k-nearest neighbor searches within a large set of poses using off-the-shelf methods. Pose averaging considering this metric can similarly be performed easily, using a projection function from the Euclidean space onto the pose space. The practical value of those theoretical developments is illustrated with an application of pose estimation of instances of a 3D rigid object given an input depth map, via a Mean Shift procedure.

Mots clés: metric; average; rotation; 3D rigid object; symmetry; Object recognition; pose estimation; distance; SO(3); SE(3); pose

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Mécanique des solides [physics.class-ph]; Physique mathématique [math-ph]; Géométrie métrique [math.MG]

Romain Brégier, Frédéric Devernay, Laetitia Leyrit, James L. Crowley. Defining the Pose of any 3D Rigid Object and an Associated Distance. International Journal of Computer Vision, 2018, 126 (6), pp.571-596. ⟨10.1007/s11263-017-1052-4⟩. ⟨hal-01415027v3⟩